Theorem 3adant3r2 843

Description: Deduction adding a conjunct to antecedent.

Hypothesis

Ref	Expression
3exp.1	|- ((ph /\ ps /\ ch) -> th)

Assertion

Ref	Expression
3adant3r2	|- ((ph /\ (ps /\ ta /\ ch)) -> th)

Proof of Theorem 3adant3r2

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 |- ((ph /\ ps /\ ch) -> th)
2	1	3expb 834	. 2 |- ((ph /\ (ps /\ ch)) -> th)
3	2	3adantr2 807	1 |- ((ph /\ (ps /\ ta /\ ch)) -> th)

Syntax hints:   -> wi 3   /\ wa 223   /\ w3a 775

This theorem is referenced by:  mettri 7817  grppnpcan2 8092  grpnnncan2 8093  ablmuldiv 8107  ablnnncan1 8113  nvmdi 8270  ipdi 8503  ipassr 8506  ipsubdir 8508  ipsubdi 8509  homgrf 10730

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 777

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